/** * @author Richard Davey * @copyright 2013-2024 Phaser Studio Inc. * @license {@link https://opensource.org/licenses/MIT|MIT License} */ // Adapted from [gl-matrix](https://github.com/toji/gl-matrix) by toji // and [vecmath](https://github.com/mattdesl/vecmath) by mattdesl var Class = require('../utils/Class'); /** * @classdesc * A representation of a vector in 3D space. * * A three-component vector. * * @class Vector3 * @memberof Phaser.Math * @constructor * @since 3.0.0 * * @param {number} [x] - The x component. * @param {number} [y] - The y component. * @param {number} [z] - The z component. */ var Vector3 = new Class({ initialize: function Vector3 (x, y, z) { /** * The x component of this Vector. * * @name Phaser.Math.Vector3#x * @type {number} * @default 0 * @since 3.0.0 */ this.x = 0; /** * The y component of this Vector. * * @name Phaser.Math.Vector3#y * @type {number} * @default 0 * @since 3.0.0 */ this.y = 0; /** * The z component of this Vector. * * @name Phaser.Math.Vector3#z * @type {number} * @default 0 * @since 3.0.0 */ this.z = 0; if (typeof x === 'object') { this.x = x.x || 0; this.y = x.y || 0; this.z = x.z || 0; } else { this.x = x || 0; this.y = y || 0; this.z = z || 0; } }, /** * Set this Vector to point up. * * Sets the y component of the vector to 1, and the others to 0. * * @method Phaser.Math.Vector3#up * @since 3.0.0 * * @return {Phaser.Math.Vector3} This Vector3. */ up: function () { this.x = 0; this.y = 1; this.z = 0; return this; }, /** * Sets the components of this Vector to be the `Math.min` result from the given vector. * * @method Phaser.Math.Vector3#min * @since 3.50.0 * * @param {Phaser.Math.Vector3} v - The Vector3 to check the minimum values against. * * @return {Phaser.Math.Vector3} This Vector3. */ min: function (v) { this.x = Math.min(this.x, v.x); this.y = Math.min(this.y, v.y); this.z = Math.min(this.z, v.z); return this; }, /** * Sets the components of this Vector to be the `Math.max` result from the given vector. * * @method Phaser.Math.Vector3#max * @since 3.50.0 * * @param {Phaser.Math.Vector3} v - The Vector3 to check the maximum values against. * * @return {Phaser.Math.Vector3} This Vector3. */ max: function (v) { this.x = Math.max(this.x, v.x); this.y = Math.max(this.y, v.y); this.z = Math.max(this.z, v.z); return this; }, /** * Make a clone of this Vector3. * * @method Phaser.Math.Vector3#clone * @since 3.0.0 * * @return {Phaser.Math.Vector3} A new Vector3 object containing this Vectors values. */ clone: function () { return new Vector3(this.x, this.y, this.z); }, /** * Adds the two given Vector3s and sets the results into this Vector3. * * @method Phaser.Math.Vector3#addVectors * @since 3.50.0 * * @param {Phaser.Math.Vector3} a - The first Vector to add. * @param {Phaser.Math.Vector3} b - The second Vector to add. * * @return {Phaser.Math.Vector3} This Vector3. */ addVectors: function (a, b) { this.x = a.x + b.x; this.y = a.y + b.y; this.z = a.z + b.z; return this; }, /** * Calculate the cross (vector) product of two given Vectors. * * @method Phaser.Math.Vector3#crossVectors * @since 3.0.0 * * @param {Phaser.Math.Vector3} a - The first Vector to multiply. * @param {Phaser.Math.Vector3} b - The second Vector to multiply. * * @return {Phaser.Math.Vector3} This Vector3. */ crossVectors: function (a, b) { var ax = a.x; var ay = a.y; var az = a.z; var bx = b.x; var by = b.y; var bz = b.z; this.x = ay * bz - az * by; this.y = az * bx - ax * bz; this.z = ax * by - ay * bx; return this; }, /** * Check whether this Vector is equal to a given Vector. * * Performs a strict equality check against each Vector's components. * * @method Phaser.Math.Vector3#equals * @since 3.0.0 * * @param {Phaser.Math.Vector3} v - The Vector3 to compare against. * * @return {boolean} True if the two vectors strictly match, otherwise false. */ equals: function (v) { return ((this.x === v.x) && (this.y === v.y) && (this.z === v.z)); }, /** * Copy the components of a given Vector into this Vector. * * @method Phaser.Math.Vector3#copy * @since 3.0.0 * * @param {(Phaser.Math.Vector2|Phaser.Math.Vector3)} src - The Vector to copy the components from. * * @return {Phaser.Math.Vector3} This Vector3. */ copy: function (src) { this.x = src.x; this.y = src.y; this.z = src.z || 0; return this; }, /** * Set the `x`, `y`, and `z` components of this Vector to the given `x`, `y`, and `z` values. * * @method Phaser.Math.Vector3#set * @since 3.0.0 * * @param {(number|object)} x - The x value to set for this Vector, or an object containing x, y and z components. * @param {number} [y] - The y value to set for this Vector. * @param {number} [z] - The z value to set for this Vector. * * @return {Phaser.Math.Vector3} This Vector3. */ set: function (x, y, z) { if (typeof x === 'object') { this.x = x.x || 0; this.y = x.y || 0; this.z = x.z || 0; } else { this.x = x || 0; this.y = y || 0; this.z = z || 0; } return this; }, /** * Sets the components of this Vector3 from the position of the given Matrix4. * * @method Phaser.Math.Vector3#setFromMatrixPosition * @since 3.50.0 * * @param {Phaser.Math.Matrix4} mat4 - The Matrix4 to get the position from. * * @return {Phaser.Math.Vector3} This Vector3. */ setFromMatrixPosition: function (m) { return this.fromArray(m.val, 12); }, /** * Sets the components of this Vector3 from the Matrix4 column specified. * * @method Phaser.Math.Vector3#setFromMatrixColumn * @since 3.50.0 * * @param {Phaser.Math.Matrix4} mat4 - The Matrix4 to get the column from. * @param {number} index - The column index. * * @return {Phaser.Math.Vector3} This Vector3. */ setFromMatrixColumn: function (mat4, index) { return this.fromArray(mat4.val, index * 4); }, /** * Sets the components of this Vector3 from the given array, based on the offset. * * Vector3.x = array[offset] * Vector3.y = array[offset + 1] * Vector3.z = array[offset + 2] * * @method Phaser.Math.Vector3#fromArray * @since 3.50.0 * * @param {number[]} array - The array of values to get this Vector from. * @param {number} [offset=0] - The offset index into the array. * * @return {Phaser.Math.Vector3} This Vector3. */ fromArray: function (array, offset) { if (offset === undefined) { offset = 0; } this.x = array[offset]; this.y = array[offset + 1]; this.z = array[offset + 2]; return this; }, /** * Add a given Vector to this Vector. Addition is component-wise. * * @method Phaser.Math.Vector3#add * @since 3.0.0 * * @param {(Phaser.Math.Vector2|Phaser.Math.Vector3)} v - The Vector to add to this Vector. * * @return {Phaser.Math.Vector3} This Vector3. */ add: function (v) { this.x += v.x; this.y += v.y; this.z += v.z || 0; return this; }, /** * Add the given value to each component of this Vector. * * @method Phaser.Math.Vector3#addScalar * @since 3.50.0 * * @param {number} s - The amount to add to this Vector. * * @return {Phaser.Math.Vector3} This Vector3. */ addScalar: function (s) { this.x += s; this.y += s; this.z += s; return this; }, /** * Add and scale a given Vector to this Vector. Addition is component-wise. * * @method Phaser.Math.Vector3#addScale * @since 3.50.0 * * @param {(Phaser.Math.Vector2|Phaser.Math.Vector3)} v - The Vector to add to this Vector. * @param {number} scale - The amount to scale `v` by. * * @return {Phaser.Math.Vector3} This Vector3. */ addScale: function (v, scale) { this.x += v.x * scale; this.y += v.y * scale; this.z += v.z * scale || 0; return this; }, /** * Subtract the given Vector from this Vector. Subtraction is component-wise. * * @method Phaser.Math.Vector3#subtract * @since 3.0.0 * * @param {(Phaser.Math.Vector2|Phaser.Math.Vector3)} v - The Vector to subtract from this Vector. * * @return {Phaser.Math.Vector3} This Vector3. */ subtract: function (v) { this.x -= v.x; this.y -= v.y; this.z -= v.z || 0; return this; }, /** * Perform a component-wise multiplication between this Vector and the given Vector. * * Multiplies this Vector by the given Vector. * * @method Phaser.Math.Vector3#multiply * @since 3.0.0 * * @param {(Phaser.Math.Vector2|Phaser.Math.Vector3)} v - The Vector to multiply this Vector by. * * @return {Phaser.Math.Vector3} This Vector3. */ multiply: function (v) { this.x *= v.x; this.y *= v.y; this.z *= v.z || 1; return this; }, /** * Scale this Vector by the given value. * * @method Phaser.Math.Vector3#scale * @since 3.0.0 * * @param {number} scale - The value to scale this Vector by. * * @return {Phaser.Math.Vector3} This Vector3. */ scale: function (scale) { if (isFinite(scale)) { this.x *= scale; this.y *= scale; this.z *= scale; } else { this.x = 0; this.y = 0; this.z = 0; } return this; }, /** * Perform a component-wise division between this Vector and the given Vector. * * Divides this Vector by the given Vector. * * @method Phaser.Math.Vector3#divide * @since 3.0.0 * * @param {(Phaser.Math.Vector2|Phaser.Math.Vector3)} v - The Vector to divide this Vector by. * * @return {Phaser.Math.Vector3} This Vector3. */ divide: function (v) { this.x /= v.x; this.y /= v.y; this.z /= v.z || 1; return this; }, /** * Negate the `x`, `y` and `z` components of this Vector. * * @method Phaser.Math.Vector3#negate * @since 3.0.0 * * @return {Phaser.Math.Vector3} This Vector3. */ negate: function () { this.x = -this.x; this.y = -this.y; this.z = -this.z; return this; }, /** * Calculate the distance between this Vector and the given Vector. * * @method Phaser.Math.Vector3#distance * @since 3.0.0 * * @param {(Phaser.Math.Vector2|Phaser.Math.Vector3)} v - The Vector to calculate the distance to. * * @return {number} The distance from this Vector to the given Vector. */ distance: function (v) { var dx = v.x - this.x; var dy = v.y - this.y; var dz = v.z - this.z || 0; return Math.sqrt(dx * dx + dy * dy + dz * dz); }, /** * Calculate the distance between this Vector and the given Vector, squared. * * @method Phaser.Math.Vector3#distanceSq * @since 3.0.0 * * @param {(Phaser.Math.Vector2|Phaser.Math.Vector3)} v - The Vector to calculate the distance to. * * @return {number} The distance from this Vector to the given Vector, squared. */ distanceSq: function (v) { var dx = v.x - this.x; var dy = v.y - this.y; var dz = v.z - this.z || 0; return dx * dx + dy * dy + dz * dz; }, /** * Calculate the length (or magnitude) of this Vector. * * @method Phaser.Math.Vector3#length * @since 3.0.0 * * @return {number} The length of this Vector. */ length: function () { var x = this.x; var y = this.y; var z = this.z; return Math.sqrt(x * x + y * y + z * z); }, /** * Calculate the length of this Vector squared. * * @method Phaser.Math.Vector3#lengthSq * @since 3.0.0 * * @return {number} The length of this Vector, squared. */ lengthSq: function () { var x = this.x; var y = this.y; var z = this.z; return x * x + y * y + z * z; }, /** * Normalize this Vector. * * Makes the vector a unit length vector (magnitude of 1) in the same direction. * * @method Phaser.Math.Vector3#normalize * @since 3.0.0 * * @return {Phaser.Math.Vector3} This Vector3. */ normalize: function () { var x = this.x; var y = this.y; var z = this.z; var len = x * x + y * y + z * z; if (len > 0) { len = 1 / Math.sqrt(len); this.x = x * len; this.y = y * len; this.z = z * len; } return this; }, /** * Calculate the dot product of this Vector and the given Vector. * * @method Phaser.Math.Vector3#dot * @since 3.0.0 * * @param {Phaser.Math.Vector3} v - The Vector3 to dot product with this Vector3. * * @return {number} The dot product of this Vector and `v`. */ dot: function (v) { return this.x * v.x + this.y * v.y + this.z * v.z; }, /** * Calculate the cross (vector) product of this Vector (which will be modified) and the given Vector. * * @method Phaser.Math.Vector3#cross * @since 3.0.0 * * @param {Phaser.Math.Vector3} v - The Vector to cross product with. * * @return {Phaser.Math.Vector3} This Vector3. */ cross: function (v) { var ax = this.x; var ay = this.y; var az = this.z; var bx = v.x; var by = v.y; var bz = v.z; this.x = ay * bz - az * by; this.y = az * bx - ax * bz; this.z = ax * by - ay * bx; return this; }, /** * Linearly interpolate between this Vector and the given Vector. * * Interpolates this Vector towards the given Vector. * * @method Phaser.Math.Vector3#lerp * @since 3.0.0 * * @param {Phaser.Math.Vector3} v - The Vector3 to interpolate towards. * @param {number} [t=0] - The interpolation percentage, between 0 and 1. * * @return {Phaser.Math.Vector3} This Vector3. */ lerp: function (v, t) { if (t === undefined) { t = 0; } var ax = this.x; var ay = this.y; var az = this.z; this.x = ax + t * (v.x - ax); this.y = ay + t * (v.y - ay); this.z = az + t * (v.z - az); return this; }, /** * Takes a Matrix3 and applies it to this Vector3. * * @method Phaser.Math.Vector3#applyMatrix3 * @since 3.50.0 * * @param {Phaser.Math.Matrix3} mat3 - The Matrix3 to apply to this Vector3. * * @return {Phaser.Math.Vector3} This Vector3. */ applyMatrix3: function (mat3) { var x = this.x; var y = this.y; var z = this.z; var m = mat3.val; this.x = m[0] * x + m[3] * y + m[6] * z; this.y = m[1] * x + m[4] * y + m[7] * z; this.z = m[2] * x + m[5] * y + m[8] * z; return this; }, /** * Takes a Matrix4 and applies it to this Vector3. * * @method Phaser.Math.Vector3#applyMatrix4 * @since 3.50.0 * * @param {Phaser.Math.Matrix4} mat4 - The Matrix4 to apply to this Vector3. * * @return {Phaser.Math.Vector3} This Vector3. */ applyMatrix4: function (mat4) { var x = this.x; var y = this.y; var z = this.z; var m = mat4.val; var w = 1 / (m[3] * x + m[7] * y + m[11] * z + m[15]); this.x = (m[0] * x + m[4] * y + m[8] * z + m[12]) * w; this.y = (m[1] * x + m[5] * y + m[9] * z + m[13]) * w; this.z = (m[2] * x + m[6] * y + m[10] * z + m[14]) * w; return this; }, /** * Transform this Vector with the given Matrix. * * @method Phaser.Math.Vector3#transformMat3 * @since 3.0.0 * * @param {Phaser.Math.Matrix3} mat - The Matrix3 to transform this Vector3 with. * * @return {Phaser.Math.Vector3} This Vector3. */ transformMat3: function (mat) { var x = this.x; var y = this.y; var z = this.z; var m = mat.val; this.x = x * m[0] + y * m[3] + z * m[6]; this.y = x * m[1] + y * m[4] + z * m[7]; this.z = x * m[2] + y * m[5] + z * m[8]; return this; }, /** * Transform this Vector with the given Matrix4. * * @method Phaser.Math.Vector3#transformMat4 * @since 3.0.0 * * @param {Phaser.Math.Matrix4} mat - The Matrix4 to transform this Vector3 with. * * @return {Phaser.Math.Vector3} This Vector3. */ transformMat4: function (mat) { var x = this.x; var y = this.y; var z = this.z; var m = mat.val; this.x = m[0] * x + m[4] * y + m[8] * z + m[12]; this.y = m[1] * x + m[5] * y + m[9] * z + m[13]; this.z = m[2] * x + m[6] * y + m[10] * z + m[14]; return this; }, /** * Transforms the coordinates of this Vector3 with the given Matrix4. * * @method Phaser.Math.Vector3#transformCoordinates * @since 3.0.0 * * @param {Phaser.Math.Matrix4} mat - The Matrix4 to transform this Vector3 with. * * @return {Phaser.Math.Vector3} This Vector3. */ transformCoordinates: function (mat) { var x = this.x; var y = this.y; var z = this.z; var m = mat.val; var tx = (x * m[0]) + (y * m[4]) + (z * m[8]) + m[12]; var ty = (x * m[1]) + (y * m[5]) + (z * m[9]) + m[13]; var tz = (x * m[2]) + (y * m[6]) + (z * m[10]) + m[14]; var tw = (x * m[3]) + (y * m[7]) + (z * m[11]) + m[15]; this.x = tx / tw; this.y = ty / tw; this.z = tz / tw; return this; }, /** * Transform this Vector with the given Quaternion. * * @method Phaser.Math.Vector3#transformQuat * @since 3.0.0 * * @param {Phaser.Math.Quaternion} q - The Quaternion to transform this Vector with. * * @return {Phaser.Math.Vector3} This Vector3. */ transformQuat: function (q) { // benchmarks: http://jsperf.com/quaternion-transform-vec3-implementations var x = this.x; var y = this.y; var z = this.z; var qx = q.x; var qy = q.y; var qz = q.z; var qw = q.w; // calculate quat * vec var ix = qw * x + qy * z - qz * y; var iy = qw * y + qz * x - qx * z; var iz = qw * z + qx * y - qy * x; var iw = -qx * x - qy * y - qz * z; // calculate result * inverse quat this.x = ix * qw + iw * -qx + iy * -qz - iz * -qy; this.y = iy * qw + iw * -qy + iz * -qx - ix * -qz; this.z = iz * qw + iw * -qz + ix * -qy - iy * -qx; return this; }, /** * Multiplies this Vector3 by the specified matrix, applying a W divide. This is useful for projection, * e.g. unprojecting a 2D point into 3D space. * * @method Phaser.Math.Vector3#project * @since 3.0.0 * * @param {Phaser.Math.Matrix4} mat - The Matrix4 to multiply this Vector3 with. * * @return {Phaser.Math.Vector3} This Vector3. */ project: function (mat) { var x = this.x; var y = this.y; var z = this.z; var m = mat.val; var a00 = m[0]; var a01 = m[1]; var a02 = m[2]; var a03 = m[3]; var a10 = m[4]; var a11 = m[5]; var a12 = m[6]; var a13 = m[7]; var a20 = m[8]; var a21 = m[9]; var a22 = m[10]; var a23 = m[11]; var a30 = m[12]; var a31 = m[13]; var a32 = m[14]; var a33 = m[15]; var lw = 1 / (x * a03 + y * a13 + z * a23 + a33); this.x = (x * a00 + y * a10 + z * a20 + a30) * lw; this.y = (x * a01 + y * a11 + z * a21 + a31) * lw; this.z = (x * a02 + y * a12 + z * a22 + a32) * lw; return this; }, /** * Multiplies this Vector3 by the given view and projection matrices. * * @method Phaser.Math.Vector3#projectViewMatrix * @since 3.50.0 * * @param {Phaser.Math.Matrix4} viewMatrix - A View Matrix. * @param {Phaser.Math.Matrix4} projectionMatrix - A Projection Matrix. * * @return {Phaser.Math.Vector3} This Vector3. */ projectViewMatrix: function (viewMatrix, projectionMatrix) { return this.applyMatrix4(viewMatrix).applyMatrix4(projectionMatrix); }, /** * Multiplies this Vector3 by the given inversed projection matrix and world matrix. * * @method Phaser.Math.Vector3#unprojectViewMatrix * @since 3.50.0 * * @param {Phaser.Math.Matrix4} projectionMatrix - An inversed Projection Matrix. * @param {Phaser.Math.Matrix4} worldMatrix - A World View Matrix. * * @return {Phaser.Math.Vector3} This Vector3. */ unprojectViewMatrix: function (projectionMatrix, worldMatrix) { return this.applyMatrix4(projectionMatrix).applyMatrix4(worldMatrix); }, /** * Unproject this point from 2D space to 3D space. * The point should have its x and y properties set to * 2D screen space, and the z either at 0 (near plane) * or 1 (far plane). The provided matrix is assumed to already * be combined, i.e. projection * view * model. * * After this operation, this vector's (x, y, z) components will * represent the unprojected 3D coordinate. * * @method Phaser.Math.Vector3#unproject * @since 3.0.0 * * @param {Phaser.Math.Vector4} viewport - Screen x, y, width and height in pixels. * @param {Phaser.Math.Matrix4} invProjectionView - Combined projection and view matrix. * * @return {Phaser.Math.Vector3} This Vector3. */ unproject: function (viewport, invProjectionView) { var viewX = viewport.x; var viewY = viewport.y; var viewWidth = viewport.z; var viewHeight = viewport.w; var x = this.x - viewX; var y = (viewHeight - this.y - 1) - viewY; var z = this.z; this.x = (2 * x) / viewWidth - 1; this.y = (2 * y) / viewHeight - 1; this.z = 2 * z - 1; return this.project(invProjectionView); }, /** * Make this Vector the zero vector (0, 0, 0). * * @method Phaser.Math.Vector3#reset * @since 3.0.0 * * @return {Phaser.Math.Vector3} This Vector3. */ reset: function () { this.x = 0; this.y = 0; this.z = 0; return this; } }); /** * A static zero Vector3 for use by reference. * * This constant is meant for comparison operations and should not be modified directly. * * @constant * @name Phaser.Math.Vector3.ZERO * @type {Phaser.Math.Vector3} * @since 3.16.0 */ Vector3.ZERO = new Vector3(); /** * A static right Vector3 for use by reference. * * This constant is meant for comparison operations and should not be modified directly. * * @constant * @name Phaser.Math.Vector3.RIGHT * @type {Phaser.Math.Vector3} * @since 3.16.0 */ Vector3.RIGHT = new Vector3(1, 0, 0); /** * A static left Vector3 for use by reference. * * This constant is meant for comparison operations and should not be modified directly. * * @constant * @name Phaser.Math.Vector3.LEFT * @type {Phaser.Math.Vector3} * @since 3.16.0 */ Vector3.LEFT = new Vector3(-1, 0, 0); /** * A static up Vector3 for use by reference. * * This constant is meant for comparison operations and should not be modified directly. * * @constant * @name Phaser.Math.Vector3.UP * @type {Phaser.Math.Vector3} * @since 3.16.0 */ Vector3.UP = new Vector3(0, -1, 0); /** * A static down Vector3 for use by reference. * * This constant is meant for comparison operations and should not be modified directly. * * @constant * @name Phaser.Math.Vector3.DOWN * @type {Phaser.Math.Vector3} * @since 3.16.0 */ Vector3.DOWN = new Vector3(0, 1, 0); /** * A static forward Vector3 for use by reference. * * This constant is meant for comparison operations and should not be modified directly. * * @constant * @name Phaser.Math.Vector3.FORWARD * @type {Phaser.Math.Vector3} * @since 3.16.0 */ Vector3.FORWARD = new Vector3(0, 0, 1); /** * A static back Vector3 for use by reference. * * This constant is meant for comparison operations and should not be modified directly. * * @constant * @name Phaser.Math.Vector3.BACK * @type {Phaser.Math.Vector3} * @since 3.16.0 */ Vector3.BACK = new Vector3(0, 0, -1); /** * A static one Vector3 for use by reference. * * This constant is meant for comparison operations and should not be modified directly. * * @constant * @name Phaser.Math.Vector3.ONE * @type {Phaser.Math.Vector3} * @since 3.16.0 */ Vector3.ONE = new Vector3(1, 1, 1); module.exports = Vector3;